The action is being led by Marwan Barghouti, a Palestinian leader jailed by Israel for life for five murders.
Barghouti, a key figure in Palestinian President Mahmoud Abbas’ Fatah faction, has been touted as a possible future successor to Mr Abbas.
There are fears the protest could fuel tensions across the occupied West Bank.
According to Israel’s prison service, 1,187 Palestinians in Israeli prisons are joining the hunger strike, which coincides with the annual Palestinian Prisoners Day.
The issue of Palestinians held in Israeli jails is an ongoing source of tension between the two sides.
Palestinians regard the detainees as political prisoners, many of whom have been convicted of attacks against Israeli and other offences.
Others are detained under so-called Administrative Detention, which allows suspects to be held without charge for six-month intervals.
There were about 7,000 Palestinians held in Israeli jails by the end of last year, according to Palestinian prisoners’ groups.
